Multivariate Polynomials, Duality and Structured Matrices

Bernard Mourrain 1 Victor Y. Pan
1 SAGA - Algebraic Systems, Geometry and Applications
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We re-investigate the well known classes of Toeplitz, Hankel, Vandermonde, and other related structured matrices, by re-examining their correlations to operations with univariate polynomials. Then we show some natural extensions of such classes of matrices based on the correlations to multivariate polynomials. We describe these correlations in terms of the associated operators of multiplication in the polynomial ring and its dual, which allows us to generalize these structures to the multivariate case. Multivariate Toeplitz, Hankel, and Vandermonde matrices, Bezoutians, algebraic residues and relations between them are studied. Finally, we show some applications of structured matrices to root finding problems for a system of multivariate polynomial equations, where these matrices play an important role. The developed techniques enable us to obtain a better insight into the major problems of multivariate polynomial computations and to improve substantially the known techniques of the study of these major problems.
Document type :
Reports
Complete list of metadatas

Cited literature [1 references]  Display  Hide  Download

https://hal.inria.fr/inria-00073171
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 12:02:49 PM
Last modification on : Saturday, January 27, 2018 - 1:31:31 AM
Long-term archiving on : Sunday, April 4, 2010 - 9:42:59 PM

Identifiers

  • HAL Id : inria-00073171, version 1

Collections

Citation

Bernard Mourrain, Victor Y. Pan. Multivariate Polynomials, Duality and Structured Matrices. RR-3513, INRIA. 1998. ⟨inria-00073171⟩

Share

Metrics

Record views

212

Files downloads

480